liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
University of Michigan, MI 48109 USA.
University of Leicester, England.
2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 21-22, 3710-3714 p.Article in journal (Refereed) Published
Abstract [en]

We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 51, no 21-22, 3710-3714 p.
Keyword [en]
Contact problems; Shakedown; Melans theorem; Coulomb friction; Attractors
National Category
URN: urn:nbn:se:liu:diva-111594DOI: 10.1016/j.ijsolstr.2014.07.004ISI: 000342254800019OAI: diva2:758598
Available from: 2014-10-27 Created: 2014-10-27 Last updated: 2014-10-27

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Andersson, Lars-Erik
By organisation
Mathematics and Applied MathematicsThe Institute of Technology
In the same journal
International Journal of Solids and Structures

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 100 hits
ReferencesLink to record
Permanent link

Direct link